2, 9, 16, 23,…
The first term of the arithmetic sequence is 2. To obtain the second term, the common difference 7 is added to the first term. To get the next term, again we add the common difference to the term preceeding it and so on.
Observing the pattern above, to find the next term, multiply the common difference by one less than the number of term then add to the first term. This is the general rule of an arithmetic sequence.
an = a1 + (n - 1)d
Examples:
1. Find the 21st term of the arithmetic sequence: 4, 7, 10, 13,…
Note that a1= 4, d= 3, and n= 21. Then, using the formula, substitute the given;
a21= 4 + (21 - 1)3
a21= 4 + (20)3
a21= 4 + 60
a21= 64
Thus the 21st term is 64.
2. In the arithmetic sequence 4, 7, 10, 13,…, which term has a value of 301?
an= a1 + (n - 1)d Formula
301 = 4 + (n - 1)3 Substituting
300 = 3n
100 = n
Thus the 100th term is 301
3. The 3rd term of an arithmetic sequence is 8 and the 16th term is 47. Find d, a1 and the 71st term.
Given: a3= 8, a16= 47
a3 = a1 + (3 - 1)d
8 = a1 + (3 - 1)d
8 = a1 + 2d
a16 = a1 + (16 - 1)d
47 = a1 + (16 - 1)d
47 = a1 + 16d
Solve these two equation simultaneously for a1 and d. Subtracting the equation,
8 = a1 + 2d
[-47 = a1 + 15d]
——————————————————
-39 = -13d
3d
Using a3:
a3 = a1 + (3 - 1)3
8 = a1 + (2)(3)
2 = a1
Finding the 71st term:
a71 = a1 + (71 - 1)d
a71 = 2 + (70)3
a71 = 212
Alternative Solution:
Given: a3 = 8 (ak), a16 = 47 (an) then,
an - ak
d
= —————————
n - k
a16 - a3 47-8 38
d = ————————— = ———— = —— = 3
16 - 3 16-3 13
This formula is also applicable to find the term of the given arithmetic sequence.
YOU ARE READING
MATHEMATICS 10
Non-FictionThis book contains topics from Grade 10 Mathematics. This book might not have all the topics of Mathematics in grade 10 but it will surely help you. Use this as a guide to your Math subject but don't always depend here. Date created: May 8, 2019 Da...
